Polynomial $\mathcal{Z}$-contraction: A unified approach with Application

Abstract

In this paper, we introduce polynomial $\mathcal{Z}$-contraction by unifying the ideas of polynomial contraction and $\mathcal{Z}$-contraction and also provide demonstrative examples to show the effectiveness and novelty. Chiefly, we prove two fixed point results for polynomial $\mathcal{Z}$-contraction employing simulation functions. Lastly, we utilize our main result to discuss the existence and uniqueness of solution for boundary value problem with a concrete example in $L^p(0,\pi )$ under suitable assumptions.

arXiv comment16 pages, 1 figure(two sub figures)